Is this voltage rating relative to ground or differential?
Note that the sensor is four resistors that vary with the quantity being measured.  These resistors are arranged in a bridge configuration.  The output is the differential voltage between the two taps, and you supply a fixed voltage between top and bottom of the bridge.

The spec you are asking about is giving the limits of the fixed voltage you apply, which they are calling the excitation voltage.  Elsewhere in the same datasheet, there are wires labeled +excitation voltage and -excitation voltage.  That implies that the spec you ask about is half the end to end voltage that you apply, but it is not really clear on that point.

You say the amplifier you use applies &plusmn;10 V.  Whoever designed that amp believes the spec is half the end to end voltage.  If this amp came from the transducer manufacturer or is recommended by them, then that would clear it up.

Otherwise, the safe thing to do is to limit the end to end voltage to 12 V until you hear from the manufacturer that the spec really means you can go up to &plusmn;12 V.  Ask them.