1 Cor 14:2 clearly states that when a person speaks in tongues, he is speaking to God:
1 Cor 14:
2) For he that speaketh in an [unknown] tongue speaketh not unto men, but unto God: for no man understandeth him; howbeit in the spirit he speaketh mysteries.
28) But if there be no interpreter, let him keep silence in the church; and let him speak to himself, and to God.
In 1 Cor 14:21, Paul is quoting Isa 28:11, so the two verses are really one. Isa 28:11 is not a prophesy of speaking in tongues. It is talking about that because of Israel's disobedience, they would be conquered by the Assyrians, who would speak to the Israelites in the Assyrian language, which the Israelites did not understand.
Paul references Isa 28:11 because just as being conquered by the Assyrians should have been a sign to Israel that they had been disobedient, speaking in tongues should be a sign to people who do not believe. The point is that both are signs, not that Isaiah was prophesying about speaking in tongues.
Also, when a person speaks in tongues, that person is to be the one to interpret:
1 Cor 14:
5) I would that ye all spake with tongues, but rather that ye prophesied: for greater is he that prophesieth than he that speaketh with tongues, except he interpret, that the church may receive edifying.
13) Wherefore let him that speaketh in an [unknown] tongue pray that he may interpret.
It is my understanding that you're mixing tongues with prophesy. Someone is speaking in tongues (which is always TO God), and another is providing an "interpretation" which is actually a word of prophesy. It is through the manifestation of prophesy that:
25) And thus are the secrets of his heart made manifest; and so falling down on his face he will worship God, and report that God is in you of a truth."
While both tongues with interpretation and prophesy edify the church, I believe they do so in slightly different ways. Prophesy will be words FROM God (1st person) or speaking FOR God (3rd person) to the body of believers present (or to an individual), while tongues is words of praise and thanks TO God, and the interpretation will reflect that.
But despite our differences, I'm thrilled that you and your church are practicing the manifestations!