It is known that the RT-100 can start a tuning cycle with the Yaesu radio in ATAS mode by pressing PTT and UP button on the mike at the same time
But the mike's PTT and UP method starts a fresh tune cycle every time and doesn't use the tuner internal memory
To allow the tuner to recall the match quickly:
press the 'TUNE' button on the radio momentarily (do not keep it pressed)
you'll notice a big 'TUNE' banner appearing on the radio's screen
push the PTT briefly
if the tuner has this frequency in memory the brief PTT will be enough
press the 'TUNE' button on the radio momentarily to turn the 'TUNE' mode off
I own an FT-710, but it is reasonable to believe that this would work on any ATAS equipped Yaesu radio