The center tap of the transformer is used to balance the current on the + and - side of the transformer. As the + sinks current, the - does not and as the - sinks current, the + does not. This would cause the center tap to have constant current in an ideal environment. When the +/- signals aren't matched exactly (either through trace differences or 50 Ω resistor differences), the center tap current starts to have an AC component for when both the +/- signals are sinking current.
When you put a resistance or ferrite bead on the center tap, the voltage going into the center tap starts to change in relation to the current flow. This voltage can add distortion to the signal and can impact the link speed. It is likely that the symmetry problem may be from the resistors not being evenly matched. 49.9 Ω 1% resistors (not 10%) should be used for transmit and receive channel terminations.
Refer to "Figure 1 - Transmit Channel Connections and Terminations", and "Figure 2 - Receive Channel Connections and Terminations" of the LAN88730 QFN Rev B Schematic Checklist.