It is normal. And by normal I mean this is just what TIs are like. The A string is a fairly light gauge (a .070 I think). Most players who use "normal"/"normal/light" gauges are playing .085 and .080s. My only issue with the TIs IS that the A string is a little too bouncy/lively compared to the other strings in terms of feel, so I understand what you're saying. The lively feel mellows out a little when the set is broken in (which could be a few months depending how often you play, how much you sweat, and what's in your sweat, etc....). I'll say I find the A string is tonally similar enough to the other strings when broken in. For me it's just the feel that's a little off.
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