Yes, the app does remember your login between sessions. Deleting the app does wipe out the executable but does not clear the data file, so a reinstall still knows your credentials. Did you actually go through the logout process and then log back in? Scroll over to settings and then down to sign out. You should then see a button to Sign In that will show your account number (replace with the number/email of the account you want) and the proper password.

I have yet to combine my accounts, so I have both the MR and SPG app on my phone with each of them knowing the respective account credentials. Once I combine, then the other will be deleted, but after I go in and wipe the app data. I can only imagine what data is going out the door with old cell phones since many (me included until I proved otherwise) believing uninstall clears the data. A factory reset is the best solution.