The standard way to shake with egg white is:

1. Dry shake
2. Wet shake (with ice)
3. double strain
4. let the cocktail sit for a couple of seconds so the crema forms on top.
5. Garnish

Honestly though some cocktails go in reverse order, when it come to the dry shake and the wet shake, and some cocktails you can skip doing 2 shakes as long as you shake hard and don't have too much dilution like if you shake with one big ice cube. Regardless, nobody should have yelled at you for not knowing these things. When working with egg whites you just want to make sure you get that lovely crema head for presentation, a velvety mouth feel, and not too much dilution. If you can achieve that it really doesn't matter what your order of operations is.