If a cell on this list matches on another list, conditional format based on another column

On Master sheet, I have the ID's and group numbers in a table. As new ID's are added, this list will be updated.

On Jan sheet and will also all months on sheets, will be a running list of ID's with other info that has been removed for sterilization purposes.

What I want to do is have a conditional format that looks at column A on the month sheet and have it look back at the master sheet and then the group # that it is assigned having 3 different fill colors. So adding other ID's to the month table will auto fill it as it gets added to the table.

I have attached a sample spread sheet of what I am looking at doing as well as attached a picture of what I would like the final outcome of the month tab to be.

I have not yet figured out how to do this, I can label the ID's on the master tab based on its group if that helps on trying to get the ID's filled in the month tabs.