The inhaled corticosteroids, qvar beclovent nasocort pulmicort flovent et al, do not cause an appreciable change in heart rate.

That said, there are differing degrees of drug-induced tachycardia caused by the rescue drugs -- Ventolin and its purer (and more expensive version) Xopenex are believed to be the most lung-selective and the least heart-selective stimulant-wise and therefore cause the smallest increase in heart rate when compared to drugs like berotec and bricanyl.