I use a Canon 60D and am trying to connect my new YN-560-TX as a transmitter to an RF-605c as a receiver attached to my off-camera flash. It fires the light which confirms that they are connecting, but why I can't control and change the amount of light with the YN-560-TX wirelessly?
The YN-560-TX can only remotely control the power on Yongnuo's flashes that have a special radio receiver built into them: the YN-560 III, YN-560 IV, and upcoming YN-660. For all other flashes and with the RF-602 and RF-603/603II triggers, there is no remote power/zoom control, only firing the flash in sync. The RF-605 triggers add group control, but that's all.
The RF-602/603/605 triggers are manual only. They only really communicate the sync and wake-up signals (605 adds group control signals). But they don't really communicate all five of the signals on the Canon hotshoe through the contacts/pins. And it's that communication that allows for more advanced features like remote power control, TTL, and HSS.
Triggering units that offer remote power control over manual-only lights are typically tied to a specific same-brand model of flash. With Cactus V6s, it's the Cactus RF-60. With Phottix triggers, it's the Mitros+ and LumoPro LP180R, and so on.
If you want remote power control with the YN-560-TX, you either need to change your flash to a compatible Yongnuo model, or, if you're using a Canon-eTTL compatible flash, to switch from the YN-560-TX/RF-60x triggers to the YN-622C and YN-622-TX triggering units, or other eTTL-compatible or remote-power-over-manual flash triggers, like Cactus V6s, Phottix Odins, etc.