Traffic light schemes (TLSs) are commonly used to mitigate induced seismicity caused by subsurface fluid injection. Verdon and Bommer (J Seismol 25:301–326, 2021a) investigated the validity of the implicit assumptions that underpin the successful functioning of TLSs. In particular, they examined the extent to which magnitude jumps (sudden increases in event magnitudes from any preceding seismicity) and trailing events (continued increases in seismicity levels after the end of injection) took place in hydraulic fracturing (HF) induced seismicity sequences. Other technologies such as carbon capture and storage (CCS), wastewater disposal (WWD) and natural gas storage (NGS) involve the gradual but long-term injection of large fluid volumes at low pressure. Hence, we might expect to see a different spatial and temporal evolution of magnitudes for seismicity induced by low-pressure, long-term (LPLT) injections compared to HF. In this study, we compile cases of LPLT injection-induced seismicity in order to examine their temporal evolution. We examine the occurrence of magnitude jumps, trailing events and onset times for seismicity after the initiation of injection. We find that few LPLT injections have produced trailing events, and that magnitude jumps are typically below 1.5 magnitude units. The timescale of event occurrence (relative to the onset of injection) is highly variable, likely reflecting site-specific conditions. For long-term injection, we observe a trend for the largest events to occur within the earlier part of each sequence, with magnitudes then stabilising, or even reducing, as injection continues. Finally, we evaluate the performance of the next record breaking event (NRBE) model as a method for forecasting induced event magnitudes, finding that this method performs reasonably well in most cases, but that in some cases the largest event significantly exceeds this model.