We present photometric and spectroscopic observations of the unusual Type Ia supernova ASASSN-18tb, including a series of SALT spectra obtained over the course of nearly six months and the first observations of a supernova by the Transiting Exoplanet Survey Satellite (TESS). We confirm a previous observation by Kollmeier et al. (2019) showing that ASASSN-18tb is the first relatively normal Type Ia supernova to exhibit clear broad ($sim1000$ km s$^{-1}$) H$alpha$ emission in its nebular phase spectra. We find that this event is best explained as a sub-Chandrasekhar mass explosion with $M_{Ni} approx 0.3; rm{M}_odot$. Despite the strong H$alpha$ signature at late times, we find that the early rise of the supernova shows no evidence for deviations from a single-component power-law and is best fit with a moderately shallow power-law of index $1.69pm0.04$. We find that the H$alpha$ luminosity remains approximately constant after its initial detection at phase +37 d, and that the H$alpha$ velocity evolution does not trace that of the Fe~III$~lambda4660$ emission. These suggest that the H$alpha$ emission arises from circumstellar medium (CSM) rather than swept up material from a non-degenerate companion. However, ASASSN-18tb is strikingly different from other known CSM-interacting Type Ia supernovae in a number of significant ways. Those objects typically show an H$alpha$ luminosity two orders of magnitude higher than what is seen in ASASSN-18tb, pushing them away from the empirical light-curve relations that define normal Type Ia supernovae. Conversely, ASASSN-18tb exhibits a fairly typical light curve and luminosity for an underluminous or transitional SN Ia, with $M_R approx -18.1$ mag. Moreover, ASASSN-18tb is the only SN Ia showing H$alpha$ from CSM interaction to be discovered in an early-type galaxy.
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