Sorry to say, but those boards are crap. They use a single power rail from a single and noisy LM1117 LDO instead of isolating VCO and CP supply from digital and ref oscillator supply.
Two layer PCB doesnt allow you to make a good low noise synthesizer implementation based on ADF4351 with continuous ground plane, separated supply rails, good decoupling very near the IC, and a quiet loop filter. Its very easy to couple oscillator noise to loop filter and VCO supply, leading to FM modulating it and creating those sidebands.
I've analyzed some of those eBay boards and found some having 1117-5.0 regulators mistakenly mounted instead of the 3.3V version. As well as 25MHz CMOS oscillators, with high phase noise and harmonics at the output and supply ripple, instead of the more suitable clipped sinewave oscillator.
You can change the LDO and ref oscillator, and add additional capacitors. It would help, but you cant fix all the layout errors, so you will never get the ADF435x IC promised performance, as you get (or nearly) from the eval board or similar good design.