"Ar ôl iddyn nhw briodi."
Translation:After they got married.
Nothing makes it past tense! This sort of 'i-dot pattern' has no tense on its own - you have to look for the wider context:
Ar ôl iddyn nhw briodi, bydda i'n mynd ar wyliau - after they marry I will go on holiday. (They are marrying in the future, and it sounds pretty definite)
Ar ôl iddyn nhw briodi, es i ar fy ngwyliau - after they had got married I went on my holidays. (they got married in the past, before I went on hols)
Ar ôl iddyn nhw briodi, hoffwn i fynd ar wyliau - after they get married, I would like to go on hols. (looks as if they are going to get married sometime in the future, but the date might be uncertain)
Hmmm... I'm actually not sure what the tense is meant to be here since the only verb is priodi and that hasn't been conjugated.
I guess you would have to add more to the sentence to make it more clear what tense it would be.
The comparison would be that you could say in English "after marrying" which could be used in either past or present/future contexts: after marrying they went ... Or after marrying they will ....
I feel as though " ar ôl iddyn nhw wedi priodi" is wrong because the " ar ôl" and "wedi" are in the same sentence. The issue I'm finding with translating "after they are married" is because in English we use the adjective "Married" whereas the Welsh uses a verb "Priodi".