It’s entirely possible that Telperion remained sole ruler throughout her reign. But I think that the expedition to
Middle-earth was such an enormous undertaking, and so very different from anything the
Númenóreans had ever before attempted, that she probably assigned Minastir plenipotentiary powers to accomplish it. Whether he had the title “Tar” in front of his name at the time is probably not significant: even he had, he would have been keeping Telperion abreast of his preparations, and she would have remained senior ruler. By the way, I think this means that Minastir commanded the
Númenórean force in
Lindon personally: he went himself, because Telperion was still in Armenelos.
There are two other things you might bear in mind here. First, Telperion resigned her throne the same year she died. The only other Númenórean ruler to do this before Tar-Atanamir, who refused to lay down his life, was
Elros himself. I think that may indicate that either Minastir had already been declared co-regent by Telperion, or else that he was exercising such power within the kingdom that Telperion kept her title as long as she felt she could in order to spite him or remind him that she was the real sovereign. Personally, I’d like to give Telperion the benefit of the doubt and assume that she was wise and far-sighted as would befit one of the early Númenórean rulers, and that she gave Minastir some title or position that was, until that time, unusual in
Númenor so that he could do what was required of him to carry out his mission in Middle-earth.
Second, if Minastir were in charge of the preparations and expedition, it would have been “his” expedition, not his aunt’s.
You can assign the confusion to mistakes in
Tolkien’s notes. If that’s the case, he sure made the same mistakes over and over again for many years, and somehow, he uncharacteristically failed to notice them. The story makes sense if Minastir were assigned a royal title, or even made co-ruler for affairs outside Númenor, with Telperion maintaining her sovereignty on the island itself. In that case, he would have received his title while his aunt still sat on the throne, but he would not have legally exercised his power on the island of
Anadûnê itself until she retired. And the fact the he would undoubtedly have become increasingly powerful after a successful military expedition in Middle-earth that would involved almost every family in Númenor in some way or another might have irritated Telperion, so that she refused to retire.
But it’s also possible that this was a very comfortable relationship for them, and she slowly handed affairs of state over to her nephew until the effects of old age made her finally decide she’d had enough. I really think this explanation makes the most sense: it doesn’t seem that there was any friction between them, or at least we aren’t given any information about it.
Remember, too, that Ciryatan constrained his father, this same Minastir, to surrender the throne before he was ready. This might mean that Ciryatan wanted the same deal his dad got. That caused friction, and Tolkien makes a point of telling us about it.
I think the whole picture makes more sense – the expedition to Middle-earth, the conundrum about the dating of the reigns and the war, and the subsequent falling out between Minastir and Ciryatan – if Telperion and Minastir managed to find a comfortable working relationship, one that was probably unique until Narmacil I made his nephew regent in
Gondor almost 3,000 years later. I think it’s a very different situation from that of Vanimeldë, Anducal/Herucalmo, and Alcarin.