Delay then off for tone signal
The output of a 555-based astable multivibrator is a square wave, transitioning at two points on the capacitor charge / discharge curve. The output does not track the capacitor charge curve, it has a flat high and flat low. So no, the tone volume should not drop with capacitor charging. 

This is true in an ideal circuit, but there may be two caveats for the actual implementation:


If the tone circuit is entirely powered by the multivibrator's output, it is worth checking if the output of the 555 can cope with the current demand, both average and transient, of your tone generator.
Depending on the impedance of your power rails and the design of your circuit, both the tone circuit's volume, and the timing for both the oscillators, could either droop or glitch. 


Please share a schematic for more specific responses.