The core of Jupiter is metallic hydrogen - which only exists at slightly above absolute zero when it's at normal pressures. The core of Jupiter is, however, under very high pressure - which forces the hydrogen to take on its highest-density state, even though the temperature there is extremely high.

Since the mystery sea is buried very deeply under the ice, it is probably under very high pressure. Is it possible that, under high enough pressure, ice will revert to a higher-density state (liquid water) in the same way that hydrogen does?

If that's true, then the underground sea could well be liquid water, despite the temperature. However, I suspect that the mystery sea would have to be buried extremely deeply for the pressure to be "high enough".

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Alternatively, ice is a very good insulator of heat (think of igloos). If there's some geothermal activity at the bottom of this sea, then the ice above it might insulate it from the coldness of the Martian atmosphere, allowing it to remain liquid.