Assassinate ability and two-weapon fighting [duplicate]

I have been reading about this and am finding a lot of questions similar to what I’m asking, but they also all have extra components and I just want a simple answer. I think I already know but I am new to DnD so please bear with me.

I have a lvl 5 Assassin and I use two short swords. Assassinate ability says "In addition, any hit you score against a creature that is surprised is a critical hit."

Surprise condition is listed as "If you’re surprised, you can’t move or take an action on your first turn of the combat, and you can’t take a Reaction until that turn ends."

I asked my DM if that meant that if I surprise an enemy, would both my main hand and offhand crit, with only my main hand getting sneak attack?

His answer was basically, "to prevent overkill he is limiting the assassinate crit to only the attack action, and not the bonus action."

So my main attack would trigger assassinate crit, but not my bonus action attack. I don’t agree but I can’t find any official proof otherwise. I know in the end it’s his call but that seems like it really limits me, because the whole idea of an assassin is to jump them right off the bat and then go to normal fighting. I feel the RAW backs me up but I don’t want to push it.

How do I argue this? Should I argue this after he made a ruling? Am I even right? I love playing with them and don’t want to push it, but I also want to take advantage of what seems like a major class feature.

Edit- to clarify, this is standard DnD 5E from what I understand. We are using any books except UA, but I am only using XGTE and SCAG for extra stuff.