B737-800 Mechanic reported software and communications problems caused an overflight event when an actuator was not replaced on time.

Narrative

On Date; MEL 78-XX Logbook Deferral Sheet XXXXXXX was assigned on an overnight maintenance work. We were expected to replace 1 of 2 actuators. The original MEL referenced Eng #1 upper left and upper right thrust reverser actuators failed integrity tests; only 1 of the 2 monitors were noted in the MEL. After additional review it was noted monitor Logbook Deferral Sheet YYYYYYY was to replace the left sleeve upper actuator - outboard; and Logbook Deferral Sheet ZZZZZZZ was to replace the right sleeve upper actuator - inboard. The monitors were inadvertently attached to the component" and not the airframe.I communicated with planning to add Logbook Deferral Sheet YYYYYYY to the overnight maintenance work for ZZZ to replace the upper left sleeve actuator. I also had Logbook Deferral Sheet XXXXXXX unlocked for MEL deferral as we would only replace one of the 2 actuators. I updated the MEL Logbook Deferral Sheet XXXXXXX stating both monitor items had to be completed for the MEL; stating both actuators need replacement. The 3rd shift AMTs (Aviation Maintenance Technician) assigned used job card X and proceeded with removal and replacement of the upper left outboard actuator. By [the] end of shift the new actuator was partially installed [and] both a written and hands-on verbal turnover were provided to the next shift. Prior to the end of my shift; I again updated the MEL item XXXXXXX deferral. I believed the installation of the actuator would be complete and referenced YYYYYYY and wrote "replaced upper left actuator" and that the right actuator replacement was required reference ZZZZZZZ. However; the AMTs that took over the job completed the hook-up and operations and leak checks but were not able to complete the rigging due to lack of tooling.YYYYYYY was deferred and accurately updated with the open rigging steps on the job card. This Logbook Deferral Sheet was open and documented properly; and the thrust reverser still on MEL; when the aircraft departed ZZZ on Date. My MEL deferral statement above was no longer accurate as the replacement was incomplete. The actuator that was removed had remained at ZZZ and was not released for shipping due to some type of processing issue. On Date 1 the store's personnel brought this up to a Crew Chief on duty; the part change was entered on the open MEL Logbook Deferral Sheet XXXXXXX; using the same text I had entered on Date; and that MEL/Logbook Deferral Sheet remained open.Unknown to anyone at the time this part change entry automatically triggered Logbook Deferral Sheet YYYYYYY to be changed from Aircraft X to a mock Aircraft Y. This is an automatic process within the Company system that has created a significant problem at this point; the repetitive check deferral was no longer attached to Aircraft X. This automatic process may be due to attaching the repetitive check deferral to the component; but I do not know this for sure.The right actuator was replaced on Date 2 and since the open repetitive check deferral for the rigging of the left actuator was no longer attached to the Aircraft X; the MEL was cleared. This created an overfly of the open repetitive check deferral. This automated process which sent the repetitive check deferral to the mock aircraft created the failure generating the overfly. This issue started with the lack of tooling in ZZZ needed to complete the replacement of the upper left actuator. The only reason it was deferred after installation was lack of tooling to confirm rigging. Secondarily; the process rolled the open repetitive check deferral to a mock Aircraft Y when a parts change [that] was entered was flawed. It is possible this would not have occurred if the repetitive check deferrals were attached to the aircraft; not the component.Suggestions to avoid recurrence. Have adequate tooling for aircraft maintenance. Ensure Line Maintenance uses the airframe selection for repetitive check deferrals. Attaching to component should only be for shop-level deferrals. Alter the process that rolled the item to a false/mock aircraft."