Yes. Any tiers you complete on Harb will unlock there and you'll get the rewards in the mail on Harb. Just remember to have those rewards in your inventory and not the mail when you transfer or you will lose them. Whenever you decide to transfer back, if at all considering the cost and the noticeable population difference you're about to experience on Harb, your legacy will go back and copy over the one on the Bastion and your progress will be saved so you can complete the final tiers there if you prefer.
TLDR; your progress should be exactly the same on the destination server as it was on the origin server after the transfer since the Harb legacy would now be the more progressed one.