Hi,
When you use the "update the values" action, you need to enter the value the same as it is stored in the database. So there is no point in having several "update the values" action on the same column in a mass action as only the last one will be taken into account.
The product_access level contains the ids of the user groups separated by a comma with a comma appended and another one prepended. So if you just enter the name of a user group in the field, the access level system will consider that as invalid and will discard it.
So it should like that : ,XX,YY,ZZ,
where XX, YY and ZZ are the ids of the user groups you want for your products.
Also, please note that the system will replace the value in the database by the value you enter in the field of your mass action.