When I put on fake lashes for costumes, I usually do:
Contacts, make up, lashes, make up again over lashes (touching up the eyeliner or putting more mascara on the lashes )
I don't wear make up and lashes a lot but I do wear contacts and as a rule of thumb I always put the contacts in first no matter what because I tend to use two fingers to open my eyes and one to put the contact in. Which when I have make up on messes up whatever make up I put on my eye and also my fingers are clean of any make up or glue that can hide in your fingerprints and such.
Assassin's Creed Link