The combination of positron emission tomography (PET) and magnetic resonance imaging (MRI) as a multi-modal imaging technique is considered very promising and powerful with regard to in vivo disease progression examination, therapy response monitoring and drug development. However, PET-MRI system design enabling simultaneous operation with unaffected intrinsic performance of both modalities is challenging. As one of the major issues, both the PET detectors and the MRI radio-frequency (RF) subsystem are exposed to electromagnetic (EM) interference, which may lead to PET and MRI signal-to-noise ratio (SNR) deteriorations. Early digitization of electronic PET signals within the MRI bore helps to preserve PET SNR, but occurs at the expense of increased amount of PET electronics inside the MRI and associated RF field emissions. This raises the likelihood of PET-related MRI interference by coupling into the MRI RF coil unwanted spurious signals considered as RF noise, as it degrades MRI SNR and results in MR image artefacts. RF shielding of PET detectors is a commonly used technique to reduce PET-related RF interferences, but can introduce eddy-current-related MRI disturbances and hinder the highest system integration. In this paper, we present RF interference reduction methods which rely on EM field coupling-decoupling principles of RF receive coils rather than suppressing emitted fields. By modifying clock frequencies and changing clock phase relations of digital circuits, the resulting RF field emission is optimised with regard to a lower field coupling into the MRI RF coil, thereby increasing the RF silence of PET detectors. Our methods are demonstrated by performing FPGA-based clock frequency and phase shifting of digital silicon photo-multipliers (dSiPMs) used in the PET modules of our MR-compatible Hyperion II (D) PET insert. We present simulations and magnetic-field map scans visualising the impact of altered clock phase pattern on the spatial RF field distribution, followed by MRI noise and SNR scans performed with an operating PET module using different clock frequencies and phase patterns. The methods were implemented via firmware design changes without any hardware modifications. This introduces new means of flexibility by enabling adaptive RF interference reduction optimisations in the field, e.g. when using a PET insert with different MRI systems or when different MRI RF coil types are to be operated with the same PET detector.