In order to synchronize the Time tracking fields such as Original estimate, Remaining estimate or Time spent you need to add following scripts into the corresponding synchronization processors.

Source Instance

Add the script below in the Data Filter of the Source instance to send Time tracking information to the Destination Instance.

Data filter

// Add the time tracking information to the datafilter
replica.timeSpent          = issue.timeSpent
replica.originalEstimate   = issue.originalEstimate
replica.remainingEstimate  = issue.remainingEstimate

Destination Instance

Add the script below in the Create/Change processor of the Destination instance to receive Time tracking information from the Source Instance.

Create/Change processor 

// this will overwrite the current time tracking information
issue.timeSpent   = replica.timeSpent
issue.originalEstimate   = replica.originalEstimate
issue.remainingEstimate  = replica.remainingEstimate