Is what I did correct, praying Maghrib three rak'ahs, and then completing 'Isha prayer with the Imam after that, knowing that I was traveling with the intention of fulfilling my needs and returning? And what is the correct action in such a situation?

It is permissible for a worshipper to pray Maghrib behind an Imam who is praying Isha, and he has two options: either he waits for the Imam and makes the taslim with him at the final tashahhud, or he intends to separate and makes the taslim, then joins the Imam in the last rak'ah of Isha. This difference in intention is not harmful, according to the preponderant opinion, due to a legitimate excuse.

As for a traveler who prays behind a resident, he is obligated to complete the prayer as four rak'ahs, and it is not permissible for him to shorten it.