These are the first two bars of J. S. Bach's Fughetta in c-moll (BWV 961) as edited by Henle.

Does the second trillo in the second bar start on B flat, so that it cancels the natural on the previous B? I cannot understand the second natural on the next B in that bar otherwise.

More generally, are ornaments supposed to ignore accidentals appearing in the bar and ‘see’ only the signature?