Most headphone amps uses an analog volume potentiometer or stepped attenuator up front, to pre-attenuate the input signal before it hits any active circuitry. Proper protocol is to turn this volume down when headphones are not in use. That makes it safe no matter what signal is coming in (also you are less likely to blast yourself when plugging in).
Even if that’s not the case, you’d be extremely unlikely to "fry" anything in the headphone amp, with the Makua’s maximum output of just 7.75 Volts - quite frankly any circuit which gets fried by that level of input is a bad design, with some modern balanced DACs now outputting up to 10 Volts! That said, it would be bad form to run like this without at least turning the headphone amp’s volume down. If you leave the headphone amp on and volume control up with headphones connected in such a scenario, it would be possible to fry the divers - but I’m not sure how you could ignore the horrible noise!
A few headphone amps do not pre-attenuate the signal, and in that case they should list a "maximum input level" specification. You’d want to check that, and heed it. If it’s listed as "Infinite", then that means the analog volume control comes first in the circuit, and "volume down" is the way to go for safety.