You have 2 or 3 options, depending upon exactly what you desire:
1) Start by recording your Alesis sounds into Pro Tools, in an audio track. Just like you would a normal tape recorder. To do so, you have to set up your Pro Tools Track to record in Audio. And of course, the drum machine will be what is recorded when you hit the Start button (on both machines).
2) You have recorded MIDI information already into Pro Tools. This means that you do not yet have any audio information. At this point, you can use Pro Tools to edit your MIDI information (i.e. move drum notes around, change the dynamics of the beats, etc.). You would do this because you are not totally happy with the drum track as it stands. Thus, you edit the information before making a live audio recording. Which comes next:
Now that your MIDI information has been pefected by you, you want to use Pro Tools to play back the MIDI file. But the question is, do you want to trigger drum sounds from within Pro Tools (requires a Drum set sample to be played from within Pro Tools), or do you want the perfected MIDI information inside Pro Tools to trigger the drums sounds inside your Alesis?
3) If you want the sounds from inside your Alesis to be recorded, you now need to create a 2nd track inside Pro Tools and make sure this track is set up to record Audio. Track #1 (the Drum track's MIDI information) is going to play back from within Pro Tools, it's MIDI Out is going to the Alesis, the audio Out from the Alesis is going to your Pro Tools Sound card IN.
Track #2 has it's input coming from the Alesis.
Hit the Record button, and while Pro Tools starts to play & record at the same time - Play the MIDI track, which in turn is playing the Alesis drum sounds, which in turn is simultaneously being recorded in Track #2 (the audio track).
or
4) You wish to record the drum sounds of some Sample Drum set from within your computer (i.e. Pro Tools is using), then what you need to do is identical to to the step above, EXCEPT that instead of sending Track #1's MIDI OUT to the Alesis, you need to set up the MIDI out to trigger the drum kit you have set up inside Pro Tools (or however you get your drum kit "live" within Pro Tools).
Hence, you still record audio into track #2, but instead of recording the Alesis' drum sounds, you will be recording the drum sounds of some Drum kit you have samples of on your computer's hard drive.
Hope this helps.
Oh, one last thing. In the old days, drum sounds from MIDI had to be recorded on channel #10, but with technology advances, all manufacturer's have figured out ways to record drum kits on any channel, but you need to check the Owner's Manual to ensure that the MIDI track you are recording on, is allowed to be a Drum channel.
If you don't know about drum channels, ask and you will get answers.