you're in the wrong section I think, this is about openembedded.

Most simple but also most ugly way would be to just leave the Keybinding as it is and change in Screens/InfoBarGenerics.py function showExtensionSelection of class InfoBarExtensions to open your plugin.

If you want a prettier way or still don't know what to do just reply

You unfortunately have to think object oriented (at least a little)

What your Code does is definitely not what you're trying to do (it tries to open the PluginBrowser when InfoBarTimeshift is initialized... in fact it is not initialized when timeshift starts - what you assumed - but when the infobar is initialized and from what I remember without checking out the code this happens only once when enigma2 is started). And InfoBarTimeshift is initialized without session as argument, therefore you won't be able to access it in this context. BUT self.session is always present when you're in InfoBarTimeshift so you can just use it without assigning it.

As I told you before you should check the mappings. The Code reads:

self["TimeshiftActions"] = HelpableActionMap(self, "InfobarTimeshiftActions",
                        {
                                "timeshiftStart": (self.startTimeshift, _("start timeshift")),  # the "yellow key"
                                "timeshiftStop": (self.stopTimeshift, _("stop timeshift"))      # currently undefined :), probably 'TV'
                        }, prio=1)

Now you know that self.startTimeshift is executed when timeshiftStart is triggered (and from the comment or better yet the keymaps we know this is triggered when yellow is pressed).

So my hackish advice for you was to just alter the called function to do what you want. In that case you would end up with something like this:

def startTimeshift(self):
        from Screens.PluginBrowser import PluginBrowser
        self.session.open(PluginBrowser)

Of course there are much better ways to do this but you have to find those out for yourself