In other word, it became called 'Onsen-manju' since it was manju sold in towns of hot springs; and Onsen-manju became a standard Japanese confectionery sold in souvenir shops or served in a Japanese-style hotel of towns of hot springs.
つまり、温泉地で売られる饅頭、ということで「温泉饅頭」と呼ばれるようになったのであり、温泉地土産や旅館で出される和菓子の定番品として定着した。