Where is your 10nf and if needed 1nf. You never said what kind of signal you where applying to the PSOC chip. Also not all capacitor are created equal. Some are better for high frequency reduction that others. Also a star ground will reduce ground loop oscillating issues.
The statement from the datasheet should be observed, because otherwise your PSoC might get damaged. Whether this oscillation comes from the Vdda voltage being slightly higher that Vddd is difficult to answer. It might be that you LDO starts oscillating when under load (the outout cap for the LP2981 must NOT be ceramic, as stated in its DS).
What you can check: test your power supply circuit with some load. Add a diode inbetween the Vddd wire so its lower than Vdda.