Probably an Italian composer.
Information provided by the musicologist and WIMA contributor, Gunther Morche:
Francis Tregian must have had access to a complete set of partbooks from a not any more existing music printing. I've contacted a number of Italian experts in madrigal sources. None of them had any specific information on Valmarano, but one of them offered a hypothesis: maybe Girolamo was member of the noble family, Valmarana-Braga. As amateure composer he may have prepared a limited printed edition of his own madrigals for private use. There were music dealers in London offering almost complete sets of Venetian printed music for sale. Therefore many of these titles can be found today in English libraries only.