Any of those other things mentioned above could be coming into play here, even a spurious signal from one or more sensors is a possibility I guess, but given what you've told us and that you mention it's really too cold to ride over there atm, I reckon it's more likely that your computer was simply telling the engine to rev a bit more than normal cos the fuel pump hadn't yet quite pressurised the system enough or cos it was a tad cold (was it a tad colder'n your usual summer riding temps?? :dontknow: ) so while the engine had
started, without those extra revs it'd either be hunting a bit or maybe running a tad lean; or maybe it was just not running fantastically/all that well on old gas? :dontknow: Regardless, I reckon it'd be the Engine Control Unit/computer was calling for more revs just to keep things running properly, as it does and should whenever necessary on first start up.... :thumbup:
Remember that these Rotax V-Twin engines rev a lot harder than the 1330's do, and also rev harder than many bikes you might be more used to in the States, so possibly unlike everything you're more familiar with, 2500 rpm
ISN'T revving all that hard at all for one of them - in fact, it's not too much higher than 'normal' idle for a Spyder V-twin; maybe possibly juuust a tad higher than the 'fast idle' that you might expect to hear from a regularly run Spyder V-Twin starting up on a cold morning; and besides, those revs are not yet high enough revs to even fully lock up the SE5's clutch!!

Just for comparison, my Rotax 998 V-Twin powered 2013 RT tends to rev a little higher than 'normal' if I start it up when it's standing in the cold , especially after it's sat for a while, altho I've never bothered to check the revs or checked how long it continues to rev like that, cos it's pretty much normal & acceptable/expected behaviour for them to rev harder in those conditions.

But if yours starts revving up hard
all the time; or revs towards 5,000 rpm on that first start-up, then those
ARE getting to be highish revs for a computer to call for on a first start; and if it starts revving over 8,000 rpm on first start up ever, then it
might be heading towards an engine run-away, but not before that! :lecturef_smilie:
So really, Dani, at my 'first glance' of all this, I don't think toese revs & the engine behaviour you are expressing concern about are really all that unlikely given the circumstances, nor should either/both be an issue for
that motor in
those conditions.... in other words, even if it does something similar on other coldish mornings &/or after you haven't ridden for a while (even just a week or so...), then I don't think you really should worry too much about it; it all sounds pretty normal, even if it's not something you've noticed or been aware of happening before! It's probably because of your week long 'enforced break' in riding followed by doing some wrenching on it that you're being a little more aware of things like this atm. :thumbup:
Sooo, I reckon you can comfortably just
Ride More, Worry Less - unless it starts getting worse or happening all the time of course!

hyea: