Snail infestation

So long story short, I recently moved my two betta tanks from on house to another. Each tank had 1 fish and 1 snail. SOMEHOW during the move, BOTH tanks managed to house a looot of baby snails. I have no clue how this has happened. My two snails never came in contact with each other during the move (mystery snails). I was wanting to get an assassination snail to fix the problem. But I don’t want my og snails to be killed. They are like 1 year old. How do I fix this ??? How did it happen ???