Uttaradi Matha's own historical materials remember Madhava Tirtha's period as the time the matha obtained one of its most treasured deities: Sri Vamsha Rama, still worshipped today alongside the matha's other sacred images, Sri Digvijaya Rama, Sri Moola Rama and Sri Moola Sita. This page reports the story exactly as that living tradition holds it -- a devotional account rather than an independently verified historical record, in keeping with this website's honest approach to material of this kind.
According to the account, Madhava Tirtha was one day engaged in the daily worship of the matha's deities when those present witnessed something unusual. In the midst of the puja he rose from his seat and prostrated with deep reverence before what appeared, to everyone else, to be empty space. When the worship was finished, he received teertha (water sanctified through worship) with visible humility from that same unseen presence. The assembled devotees, astonished, asked him to explain what they had seen.
Madhava Tirtha's answer, as the tradition preserves it, was that Madhvacharya himself had come. The founder of the sampradaya, he said, had appeared, personally worshipped the newly obtained Vamsha Rama deity, taken the sanctified water offered in worship, and then given that same teertha back to him as a blessing. For a tradition already convinced of Madhvacharya's continuing spiritual presence in the line of pontiffs he established, the story stands as evidence both of the sanctity of the Vamsha Rama deity and of Madhava Tirtha's own standing within that line.
No independent, non-devotional source corroborates the specific incident -- which is true of most such stories about pontiffs from this period, and does not by itself make the account false. It belongs, honestly, in the same category as much of what survives about Madhava Tirtha's inner life: preserved by his own tradition, cherished by his own institution, and not independently checkable by outside historical method the way his dates or his matha's founding are.