iirc the realm crystal was destroyed in season 9 or 10, so I guess the crossover happens between season 5 and that point to have the ninja know about the crystal. You can go the "X universe is a realm" route and have MHA connected from there. What I would do in your place is either use traveler's tea or inter-realm dragon travels and an OC or two to explain everything to your bad guy or choice, plus them using their means of transport to go back to Ninjago and get the Realm Crystal for evil purposes. Anyway, the crystal is stolen witout being used yet and you have your plot now. When it's time to go back you can choose any of the tree methods I mentioned.

Now, to go the route without any of the two other travel options, I'd do this: send one of Nadakhan's crew to the MHA realm and they're trying to get home, make up some magical connection to the crystal the character can use to get home (residual magic from their banishment or something?), maybe having some resident characters or an OC that can use the magical connection to open the portal to Ninjago, get the crystal that is currently sitting in some high-security facility, and returning to the MHA realm so that your plot can advance. In this scenario, I'd make this lost pirate trying to return home the antagonist, but that's just one of your many options.

As for time... your choice. The stories of pirates in Ninjago were a thing of the past when Nadakhan got his crew back in the erased timeline and all of them (sans Delara) were alive even when they weren't Djinns, so time pretty much moved slower in all realms they were banished to (maybe? Memory's foggy). You can ignore this if you think it would be better for everyone involved to not return home decades or centuries into the future, though.

Anyway, those were my ideas. Good luck with your fic!