The Main-Belt Comet P/2012 T1 (PANSTARRS) has been imaged using the 10.4 m Gran Telescopio Canarias and the 4.2 m William Herschel Telescope at six epochs in the period from 2012 November to 2013 February, with the aim of monitoring its dust environment. The dust tails' brightness and morphology are best interpreted in terms of a model of sustained dust emission spanning four to six months. The total dust mass ejected is estimated at ~6-25 × 106 kg. We assume a time-independent power-law size distribution function, with particles in the micrometer to centimeter size range. Based on the quality of the fits to the isophote fields, an anisotropic emission pattern is favored against an isotropic one, in which the particle ejection is concentrated toward high latitudes (±45° to ±90°) in a high-obliquity object (I = 80°). This seasonally driven ejection behavior, along with the modeled particle ejection velocities, are in remarkable agreement to those we found for P/2010 R2 (La Sagra).