Most chaplain hires are specific as to being non-denominational, and though a Christian chaplain may pray to Jesus, his religion is also replete with prayers to “God”, most any of which are acceptable to other faiths. By saying “Let us pray to God”, he may in his heart feel he is praying to Jesus, but a Jew in attendance will feel just as at home in praying to the Jewish interpretation of JHVH.
However, if he offers up a prayer specifically to “Jesus”, that excludes the Jew from offering his prayer to JHVH at the same time. The mainstream Jewish understanding of mashiach (the messiah) has little, if anything, in common with the Christian understanding of Jesus as Christ (Messiah). Jesus specifically doesn’t qualify as mashiach as far as Jews are concerned, any more than Sabbatai Zevi, so in effect they would consider it a prayer to a man, not God.
A Christian Reverend can either offer up a prayer to God, but as far as other non-Christian monotheistic religions are concerned, if he offers up a prayer to Jesus, it is no different than a pagan offering. They cannot pray to God at the same time as someone prays to another god at the same time.
Besides, that Jewish guy shouldn't be praying along semi-silently with the non-Jews unless he's certain that a minion of 10 is present.