How do some crossovers work?

There have been a lot of tv shows out there that have done crossovers with other shows. But the question is, how are some made to work?

It seems relatively easy to cross one show over with another when the plot device is inter-dimensional travel (Generator Rex/Ben 10: Heroes United, The Jimmy/Timmy power hour), that means that the two shows exist in two different realities, which means that anything that happened prior or after the crossover has no effect on the other show.

But when they do crossovers that establish that the two shows share the same universe (The DCAU crossovers, the Hercules/Aladdin crossover, the Lilo and Stitch crossovers, the Ben 10/Secret Saturdays crossover), it's a little hard to process at times. With shows that are comedic in nature (The Simpsons, Futurama, Family Guy, American Dad), it's much more easier to go along with; logic plays no role in their world. But in shows that have a bit more seriousness to them, it's a bit more difficult, especially when it feels like things don't add up—

What was Batman doing during the Apokalips attack?

What was Static doing during the Thanagarian invasion?

What was Jake Long doing when Dr. Drakken and the Lorwardians attacked New York (it was made clear that New York was among the cities attacked in "So the Drama" and "Graduation")

In Secret Saturdays, wasn't there a Secret Scientist whose job was to keep aliens a secret from the world? Well, if this show coincides with Ben 10 then he obviously isn't doing a very good job.

— If certain shows coexist in the same universe, then that means the big events that happened in one show were going on the in the background of another, and the latter show basically paid it no mind, which strikes me as a bit hard to believe. Plus, the elements of one show might seem a bit out of place for the setting of another—

Rugrats and The Wild Thornberrys exist in the same universe, which means that while the former show mainly focuses on the imagination of infants, it exists within a world where people can magically gain the ability to talk to animals

Any thoughts on this?

You clearly put way more thought into this than the writers do.

Well, if we follow your questions first :

What was Batman doing during the Apokalips attack? If we assume you mean during STAS, Batman was defending Gotham. Likely he started planning cosmic after that, though.

What was Static doing during the Thanagarian invasion?

• The Thanagarians had a lot of heroes on lockdown. If the League had Static and Gear's secrets, then Hawkgirl had likely betrayed those as well, either putting them on the run or in custody, like Vigilante described.*

What was Jake Long doing when Dr. Drakken and the Lorwardians attacked New York (it was made clear that New York was among the cities attacked in "So the Drama" and "Graduation")

• As a mystical guardian/warrior, Jake always has a lot on his plate. If his was anything like other shows of that sort (watched it but don't remember all) he could have been in another dimension, facing some kind of test. Maybe he was even told to stay out of it, and listened that once.*

In Secret Saturdays, wasn't there a Secret Scientist whose job was to keep aliens a secret from the world? Well, if this show coincides with Ben 10 then he obviously isn't doing a very good job.

• Maybe that division/position was retired by the time of the Xover?*

— If certain shows coexist in the same universe, then that means the big events that happened in one show were going on the in the background of another, and the latter show basically paid it no mind, which strikes me as a bit hard to believe. Plus, the elements of one show might seem a bit out of place for the setting of another—

Rugrats and The Wild Thornberrys exist in the same universe, which means that while the former show mainly focuses on the imagination of infants, it exists within a world where people can magically gain the ability to talk to animals

• Or one could posit that magical thinking, which infants have, can in some cases be carried into later years, enabling the ability to talk to animals and like that.*

Crossovers are funny things, with funny rules. Ben 10/Generator Rex requires an interdimensional link, since both have situations that are global in nature and could not coexist. A Lost In Space/Star Trek Xover would have vastly different dates for exploration landmarks, and need this as well. Rumor has it Joss Whedon killed the WB's plans for Buffy/Charmed, but even if he hadn't, the two shows have different rules on magic. Certain things would be easier. A JSA/Invaders WW 2 story could simply have the Invaders as part of the catch-all All-Star Squadron. And like that. In real life, a good friend's life might be falling apart on one coast and you might never hear about it on the other till much later. If the events are that world-shaking, then odds are the hero in the same verse needs to stay home and take care of their own area.

A Wizard Did It.

There are two main ways this is explained:

a) The characters were busy with something else at the time. Given that most of the shows crossing over are adventures, it makes sense that some stuff might have been going on that they would have helped with if only they were not busy elsewhere. It just happened "off camera."

b) The crossover happens in "a third reality" were the characters DO coexist that is NOT the official one for either universe. This was, for example, how the Marvel/DC crossovers were handled for the first few times.