Hi Tatu,
I’m using Reaper 4.10 as well, on Windows.
I don’t usually open both Toontrack Solo *and* Reaper, but just tried it while dragging a groove over (from EZdrummer within Solo) and yes, it seems to work and your description sounds consistent with what is happening on my end (i.e. the behavior so far sounds correct).

What I’ll *usually* do is open up just Reaper (not Solo), then load the Toontrack plug-in — in my case, it gives me a choice, but since you’re posting in the EZdrummer section of the forum, I’ll assume you’re looking for the EZdrummer plug-in.

If you can’t find EZdrummer in the listing of plugins within Reaper (I’m assuming you do *have* a listing of plugins in Reaper, from clicking on the FX button on a track), you can check what paths Reaper is looking through by going to…
Options > Preferences
…and then scroll down to…
Plug-ins > VST
…and the paths that Reaper is searching through for plugins should be near the top of the dialog box.
e.g. Mine says “C:Program FilesVSTPlugins”
“C:Program FilesSteinbergVSTplugins” is another common Windows location.  If you’re on Mac, it will be something else.

If you navigate to that folder and can’t find “ezdrummer.dll” within it or one of its sub-directories, then Reaper isn’t searching in the right spot.
Search your computer for “ezdrummer.dll” and then add that path to Reaper’s Preferences dialog that was opened before.

—

To hopefully help with your general confusion… Solo and Reaper can both act as “hosts” for the plugin.
Toontrack Solo hosts only Toontrack plugins, while Reaper will host multiple plugins and sorts them onto “tracks”.
You can add a MIDI groove/beat to a track in Reaper and it will play through the plugin attached to that track.
So, attach (load) the EZdrummer plugin onto a track, drop a MIDI groove onto that track, and press Play.  EZdrummer should play the groove.
Add more grooves onto the Reaper track to build a song.
And you can also rearrange and edit the grooves within Reaper.

I hope that helps!