Is it normal Allen keys are loose fitting?
They all have some play in the fit. The target outside dimensions for the most common bike hex wrench sizes (4, 5, and 6mm) are all around .1mm less than the bores they fit in, which match the nominal sizes with a tolerance of I think +/-0.05mm-ish. That shouldn't lead you to feel they're "very" loose, but they typically aren't exactly snug. Very loose suggests using imperial aka fractional/SAE wrenches, whereas virtually all Allen bolts on bikes are metric. The only exceptions I've encountered are certain 90s BMX stems.

That it's Chinese is here nor there.