proper adhesive
 

what adhesive would you recommend for a glue down vinyl application in a hot yoga studio

It all depends on the type of flooring. To say you could use a multipurpose glue might be right for the lino involved, but what temperature is this area going to be subjected to, will there be heavy traffic etc etc. There is no one answer, you should be asking this question to the manufacturer to determine if it is even suited for this kind of application. Also if it is a tile or sheet goods as the seams will play a factor on the longevity of the floor.