Can I use Shimano 105 rear derailleur from 11-speed bike with 10-speed Tiagra shifters?
TLDR: no that won't work. Tiagra 4700 was introduced in 2015 (see here), so your 2013 Allez will have 10 speed Tiagra 4600 series which is not compatible with any 11 speed derailleur.
Shifters pull a certain length of cable per gear, derailleurs have an actuation ratio. Cable pulled x actuation ratio needs to match sprocket spacing. All Shimano road groups up to 10 speed (excluding Tiagra 4700 and GRX RX400 series) used the same derailleur actuation ratio so derailleurs of different 'speeds' could be mixed and matched.
At 11 speeds the actuation ratio changed, so 11 speed derailleurs could not be used with 10 speed shifters and cassettes. The newer 10 speed Tiagra 4700 and GRX RX400 series groups are said to use the 11 speed actuation ratio so an 11 speed derailleur will work with them.
11 speed chains have slightly narrower external plates that 10 speed, so there is the possibility that a 10 speed chain will rub in a 11 speed derailleur cage.