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limit screws are correct I believe. Without any cable tension at all it sits on the smallest cog and I can push the derailleur into the biggest cog.
Shifters?
Just noticed this post, this would suggest something amiss with either cable or shifters yeah.
I'd say cable was the more likely.
If the cable is catching somewhere, be that due to corrosion, routing or damage, it could be that the shock from the ratchet mechanism clicking in the shifter is enough to sort of bump it through a bit more.
Cabling under the bar tape would be were I'd look first. How old is the set up? Have you replaced the inner and/or outer cables since new?
limit screws are correct I believe. Without any cable tension at all it sits on the smallest cog and I can push the derailleur into the biggest cog.
Shifters?