The polymer is a type of PDMS elastomer which will have crosslinking by heating.
The oil is less dense than the polymer, hence may separate due to density difference.
The oil has a quite low viscosity, lower than typical cooking oil.
They are mechanically mixed before heating, after that elevated heat is applied for the PDMS crosslinking.
As mentioned, the polymer can be crosslinked but the polymer system is not expected to chemically react with the oil. Mass of oil ~ 30% of the total mass of blend.
As far as I know, PDMS and oil are immiscible hence may have phase separation later after mixing, not to mention the effect of density difference. However, crosslinking of PDMS may stabilize the blend. I found that if oil mass is ~50% of the total blend, the phase separation appears rather quickly (visible by naked eye), even before heating is applied and the bulk of PDMS crosslinking happens.