The allocation of Digital I/O (eg on Ports usually allocated as Analog on Power-Up), TRIS and setting the I/O initial status must be the first things that your PIC does on wake up. You need ensure the minimum time is wasted from the PIC powering-up, to setting those I/O pins Low.

It could also be that you have a particularly long Start-Up (eg a lazy PSU holding the MCLR line low for too long, or a large value Capacitor on MCLR) or your POR timer value (if you have one) is too long. If you just can't get those pins Low in time, and it's a mission critical kind of operation, you may need to add additional logic between the PIC and the input pins of your Driver to inhibit output until the PIC has woken properly.