There are two kinds of FX chains on mixers: Inserts & Aux.
[Appologies if you know all this already…]
Inserts are post the preamp stage (so after mic or inst. presamp), but before the fader. They allow you to “insert” an effect on the instrument before you mix it. On a mixer with inserts, the insert is usually TRS 1/4" jack near the input. You use a Y cable, and wire it to the in & out of your effect box. Obviously, you use one effect box for each channel you want an insert on! If the mixer has digital effects, it may support one or more insert effects per channel - though often the total number effects assigned is limited.
Aux busses are essentially a separate (usually mono) mix of the channels that is then wired to your outboard effect box. The return the box may then be connected to the Aux return (if the mixer has them), or a spare channel strip. The send level on each channel strip controls the amount of that instrument that is mixed in the send to the effect, and the return is a single signal (sometimes a stereo pair) - which as you observe, doesn’t return to each channel individually. Many mixers with onboard effects have only this kind of effect system, and so the effect is applied to a “submix” of the channels.
A few digital mixers have the ability to put the effect “on the master bus”, usually, what this means is that the send to the effect is the same mix you are sending to the master mix, and then there is some control for how much of the effect your want mixed in on the way to the master outs.
You have to read the specs of mixers carefully to find out what selection of hardware insert and aux sends it has, and if it has digital effects are they insert effects or aux bus effects.
The Zoome R-16 has both insert and master effects on board - but no jacks for using outboard effects. In general, I find the R-16 effects both very hard to use, and lack luster in sound… so I never use them.