When you setup what you call a “normal template” does that mean you did not use the preset template?
What you need to know is the following:

A Cubase MIDI Track, by itself will record any and all incoming MIDI CHANNELS.
When you setup a MIDI Track the channel # setting is for MIDI Output ONLY. If you recorded a four PART Performance, which uses MIDI channels 1, 2, 3, and 4, coming In to Cubase and you then force them all back Out on channel 1 — you have a problem!

Yes that channel selection on the Midi Track is MIDI OUT. If you create one MIDI Track you need to set the channel to ANY.
ANY = each incoming channel will be thru’d back Out on the channel it arrived on.

Many folks forget that every MIDI event includes a Channel. And it only takes one MIDI Track to record all 16 Midi channels. If you press a single key on, middle “C” at a velocity of 100, on channel 1 — the message sent in hexadecimal is: 90 3C 64
9 = Note On
0 = Channel 1
3C = middle “C”, note 60
64 = velocity 100
The MONTAGE/MODX will send that same message on each linked KBD CTRL Part except that the second byte will increment to represent the Channel: 91 3C 64 for channel 2, 92 3C 64 for channel 3, and 93 3C 64 for channel 4
Cubase will re-channelized the data on the way Out from a Track... placing all four events on the same Out Channel.... unless you do one of the two following things:

1) set that MIDI track’s channel Out to “Any” — Record to a single MIDI Track
2) setup the INPUT TRANSFORMER — Record each Part to its own MIDI Track

“Any” allows the data to exit on the channel it came in on. You would DISSOLVE PARTS to split the data to separate tracks for editing... you only need separate Tracks to make it easier to look at and edit.
The ”Input Transformer” as setup by the “MODX Multi Channel Recording” Template... restricts the MIDI Channel Input to one Channel per Track and sets the corresponding MIDI Channel Out. One for each MODX Part. Neat and clean!

When you want to record a 4 Part MODX Performance you would *select* and arm a correspondingly numbered Track for each Part.
By setting the Super Knob and Scene button to send Sysex, you can capture their direct movement and engagement on their own dedicated Sysex Track. So if you intend to record Super Knob or Scene changes you can activate that track along with the 4 music Tracks.

The INPUT TRANSFORMER is key to dividing the MIDI data on the way into Cubase. Each Part you are controlling has its own discreet path to its own Track, and that Track speaks just to its own Part. Learning to set that up is a skill worth spending the 10 minutes to learn (or modify the Template to your needs). It make Cubase Pro an advantage when you are capable of transmitting from your Synthesizer on multiple MIDI Channels simultaneously.

Extra Credit
Multiple Channel transmitting allows the MONTAGE/MODX to place real-time Arpeggiators (there are 8 available simultaneously) at your disposal, each generating data on its own discreet channel/track. You can easily understand this while when playing a Performance that includes drums, how you might need that data on a separate MIDI Channel and Track. And obviously if controlling a guitar Arp and a bass Arp, how they would benefit from a discreet communication bus for their data. But also when performing an instrument sound with tons of different articulation gestures, you may want to record these to separate Tracks for detailing.

Highly recommended: master Single Part Recording before branching out to Multi Part Recording. Guaranteed you have done single Part recording previously... but Multi Part recording isn’t likely new to you. Respect the differences, particularly how to keep the data discreet.

... with non-Pro versions of Cubase I would use public-domain (free) plugins to rechannel MIDI data so Pro was not necessarily needed to gain an input-transformer type functionality. Just adding that plugins may also be a choice for rerouting the MIDI channels within Cubase.