There are many ways for this to misbehave
First of all, does the Alesis kit trigger its own sounds consistently? If it doesn't, then its likely settings for velocity and/or sensitivity in the Alesis brain. If it DOES, here are some general guidlines to consider:
1-Is the Alesis setup in the Pro Tools Midi Studio window? In Pro Tools, go to Setup>Midi>Midi Studio and create a new "instrument". Name it as you like(Edrums, Alesis, whatever). The brand and model are not crucial(IOW, if you don't see your unit listed, move on). The crucial setting is the Input Path and if you are using a USB cable from the Alesis, it would probably showup on a short dropdown list as Alesis USB[emulated] or similar. You select this so that PT knows where to "look for" incoming midi. As for midi channels, I would deselect all but channel 10(which is normally used for drums and percussion). If you are not going to use the sounds from the Alesis kit, you don't need any return path(using none will prevent possible double-triggering).
2-Xpand2 is okay, but you can do much better for a modest expense. Toontrack EZdrummer2 or XLN Addictive Drums2 are both great for use with E drums(Addictive Drums has preset mappings for Roland and Alesis kits). Not sure about EZdrummer, but back when I had my TD10 kit, mapping was 90% right out of the gate(changing mini note values for certain pads is often accomplished on the drum brain, but the plugins may also allow for that).
It may take some fussing, but it should work well