Magnetization curves and magnetic susceptibility of Tb1 xRxMn6Sn6 (R = Gd, Y) compounds have been measured for aligned powder samples. Concentration dependences of the spin-reorientation transition temperature and temperature dependences of critical fields of the field-induced magnetic transitions have been determined. For the compound Tb0.1Y0.9Mn6Sn6 with the spiral magnetic structure, we found that application of hydrostatic pressure facilitates the ferrimagnetic ordering. This unusual feature is supported by the observation of a large negative spontaneous volume magnetostriction for TbMn6Sn6. The obtained results are discussed in a model considering three different interlayer Mn-Mn exchange interactions in these compounds.