What is the correct way to seal/flash coolant lines through T1-11 siding?
Depends on where the indoor unit is that he had to connect to, in comparison of where the other were in your neighbors house.
The important thing is, the tech did slope the pipe down and out of the wall at a heck of a good angle. The only problem I really see is the type of sealant he used as a finish, unless the plan was to come back, carve off the excess foam and use that as a backer for a good brand od polyurethane caulk to finish sealing the hole where the pipe goes into the wall.

The foam does a great job of insulating around the pipe in the wall, in an otherwise difficult area to seal.

If the tech never comes back, all that is needed now is as mentioned before, is to clean the foam back enough to leave a small recess, say 1/4", not a "dished out" 1/4" but a clean, flat recess that has the edge of the cut exposed, not covered by a skin of foam, so the caulk bonds to the siding, not foam that will degrade over time by exposure. If a little more is removed than the 1/4" I spec'd, no biggy, it is just more caulk, and it will be a little less flexible.

Use tape to cover areas you do not want caulked, poly caulk is contrary, but it cleans up with paint thinner... Still messy when not prepared for it.