Tor and Firefox UI conflict

[chous]

When using Tor (4.0 binary bundle from their website) and Firefox (www-client/firefox-24.8.0) together, I experience looooong response times when using the one which launches last.

By response times I refer to responses tied to mouse clicks, anywhere, including choosing the search engine to use. After a while (~1 minute), it reacts correctly.

I don't know where should I dig into. It could be related to my X environment, but this issue does not appear with any other application. Could it be dbus, or any other process being used underneath?
I use x11-wm/xmonad-0.11-r1 + x11-wm/xmonad-contrib-0.11.2 on a 64b, xorg-server-1.15.0, with a multi-monitor setup on an ATI Radeon card.

What tests do you recommend me to do to figure out the cause of this conflict?

My best guess is that they both use some underlying framework, and messages from the second instance get sent to the wrong one. As if the first one "registers" itself and prevents the other from receiving certain messages.