Two possibilities come to mind.
1. When chain is is jumping a cog when shifting from smallest ring, it usually means cable is too tight, not too loose, so tightening the cable either by disconnecting and pulling out slack or with barrel adjuster exacerbates problem. Shift one click then, while turning crank, turn barrel adjuster slowly to loosen cable until chain settles back the second cog. Alternatively, with chain on the smallest cog, stand behind bike an check to see where derailleur cage is relative to cog. If not directly underneath the smallest cog (if cable is too tight the pulleys will be off a bit to the inboard side), loosen cable a bit with adjuster until the pulleys line up with the cog. Then click once to get chain on second cog and again ensure pulleys line up directly underneath 2nd cog via small turns of the barrel adjuster. No need to repat with rest of cogs, checking alignment with smalles two cogs should be sufficient to dial in shifting.
2. If too much cable tension is not the problem, it could be shifting technique. With trigger shifters, its pretty easy to over-shift when shifting from small cog to larger cog in the rear. Try being a bit gentler when pushing the trigger shifter to ensure you are getting just one click of the shifter with each shift.