Does heimerdinger need to be on a battlefield if Renata glasc mastermind is on one already for the tap ability?

No. Heimerdinger does not need to be at a battlefield to use Renata Glasc, Mastermind's exhaust ability — even when she's on one (and likewise when she isn't).

Heimerdinger copies the activated ability itself ("pay 4 blue, exhaust 4, exhaust self → Score 1 point") but does not inherit Renata's passive line, "Use my abilities only while I'm at a battlefield." That restriction is a separate clause of Renata's text, not part of the exhaust ability he copies (FAQ 650, 9851).

He still must pay the full cost — 4 blue runes, 4 channeled power — and he can only activate one copied ability per exhaust, since he's the single source exhausting himself (FAQ 8927).