The general rule is don't chain MIDI devices if you can avoid it.
MIDI is in modern terms, dog-slow. Each time it passes through a device it has to be completely re-transmitted, whether it is acted upon or sent onward untouched.
If you need to be transmitting to multiple devices, use a hub - one re-transmission only.
Various devices shift clock in various ways. You're never going to know how any one device is going to treat a through-stream. Some will simply echo, some will reprocess. Some where the out & through are shared in one socket will re-interpret & interleave data.
All in all, that's going to makes things lose coherence & you won't know where in the chain it's happening.
It's actually been so many years since I ever had to do anything like this I couldn't even hope to recommend anything modern to achieve this. I actually still have my Yamaha MJC8 from the mid 90s, which is about the last time I ever had to route MIDI ;)
You can actually pour 16 channels of complex midi down one pipe & have everything appear to retain its timing. Unless you have the manufacturer figures for how each channel & message is prioritised you may need to do some of this by empiricism.
The basic rules are:-
Send drums absolutely on-beat [unless your data-streaming is getting so hideously complex you even have to start shifting hi-hats ;) Many multi-timbral instruments prioritise ch10 over all others [then 1, 2, 3 … 16 in that order), so send drums on 10 if you don't know how a device prioritises.
Send other fast attacks immediately after drums [or before if things get laggy - you can't send them all together, MIDI is serial] on low-numbered channels.
Send slow attacks early, so they feel on-beat, on high channels.
Send any other data - controllers & especially Sys-Ex - miles away from any significant beat.
Once you figure these out roughly for your devices then you can just use your DAW's delays structure to save having to do it all manually.
In the old days we used to have to do this in a MIDI File itself, so playback was ensured to be tight.
I occasionally like to drag out this old demo to show just how tight it was possible to get MIDI, if you knew what you were doing. This track was tweaked entirely by hand & what you hear is untouched playback of 16 simultaneous channels from one single device, over one cable, simply recorded directly from the stereo outs. No external FX, nothing touched, except a tiny bit of finalisation comp & EQ.
Some of the sounds themselves are of course, a bit 90s sounding now, but I still think we got the brass pretty darn good even for its age ;))
We had the benefit of the exact data on the unit itself from the manufacturer, so we could literally move data by the correct number of ticks to precise milliseconds to keep the data-flow optimised. You're unlikely to find that data outside the manufacturer. [To this day I can still hear one beat that lags about 3/4 of the way through the track that we could never truly fix.]
It's probably not truly apparent just from a casual listen to the full stereo mix, but we have at least 60 instruments going, squeezed byte by byte into 16 midi channels (the brass, for instance is not just "brass section" it's separate instruments). There's also a colossal amount of controller data & Sys-Ex flying around to control filters [eg for the wah-wah guitar, it's all done on the filters], bends, FX & mixer data.
Soundcloud used to inline on here like YouTube does, but for some reason it stopped doing that in the past year, so you've to click through these days. Sorry.
BTW, the myth that some sequencers were tighter than others was just that; a myth. So long as it could clock [which technology has been able to do since the first digital watches in the 70s] most misinterpretations of a sequencer or synth's timing was based on not understanding how to shape the data flow.