I selected the individual channel strips and went to Midi Input->Multitimbral->Axiom 49->(MIDI channel 1 for keyboard channel and MIDI channel 10 for drum instrument channel)
This is the problem: you have assigned 1 channel strip to receive MIDI info from one controller (Axiom) on BOTH MIDI channels. The MultiTimbral selection "re-channelises" the connection to the channel strip, not separates according to input MIDI channel.
First, you need to have the Axiom transmit on 2 separate channels at the same time (ch 1 for the keys, ch 10 for the Pads (not sure that it can do this, check the manual, and check that it is transmitting correctly using the MIDI activity display in MS).
You will need to make 2 keyboards or Activity controls (Axiom1 and Axiom2) in Layout mode, one assigned to Axiom ch 1, the other Axiom ch 10.
In Edit mode, assign your "keys" channel strip to Axiom1, and the "drums" strip to Axiom2