Actively mode-locked fiber ring lasers (AMLLs) can generate MHz repetition rates and picosecond optical pulsewidths using an external RF signal. It makes them suitable for optical imaging and spectroscopy techniques involving multiple lasers in synchronization. However, in such systems, it is critical to address RF modulation frequency detuning for optimal performance. An AMLL is subject to RF detuning around the fundamental frequency, f_0. We extend the standard model of the mode-locked laser based on perturbative analysis and injection locking theory. The model shows a decrease in the number of cavity modes with phase-lock as detuning is increased. For a mode n, the injection range R_n / n−1, making higher modes susceptible to lock-loss due to detuning. Experimental verification of these theoretical predictions was obtained using a custom built Yb3+ doped AMLL with a fundamental frequency f_0 = 26 MHz, operating at 1064 nm. Unlocking of modes was studied in the electrical domain by varying the RF detuning over a range of ±13 kHz with a step-size of 200 Hz. The fundamental mode, n = 1, had an injection range R_1 = 143.4 kHz, with higher order modes having smaller injection ranges as predicted by the model. The model was extended to RF detuning around the harmonics of f_0, to obtain a relation between the RF detuning and the properties of the output optical pulse train. With increasing detuning, |∆_n|, the pulsewidth was found to increase as sqrt(|∆_n|) and peak power decrease with 1/|∆_n|. The same is verified experimentally for fundamental and harmonic (3rd) cases, where the minimum pulsewidths were observed to be 205 ps and 69 ps, respectively. To mitigate phase mismatch between the cavity modes and the injection signal, and achieve relocking of modes when AMLL is operated in detuned conditions, multiple RF inputs were added at the input. The theoretical model was extended to include multiple RF inputs with constant phase relationship. For experimental validation, two RF sinusoidal signals with constant phase and equal amplitude were used. For mode n = 10 an extension of the range by X_n = 6.4 kHz was achieved with two inputs compared to R_n = 14.34 kHz with single input. An increase in injection range was also observed for higher modes.