We have developed a 3D reverse time migration (RTM) implementation, with an extended imaging condition, in the presence of tilted transverse isotropy (TTI), using finite-difference time-domain solvers on the rotated staggered grid (RSG) and the Lebedev grid. We have evaluated dispersion analysis of both schemes for a sample TTI medium. Using synthetic and real seismic data in realistic execution configurations, we found surprising inconsistency with quantitative cost estimates in the literature. For fixed accuracy, the RSG scheme proved most efficient in our tests, and not two to three times less efficient, as had been posited. Of course, variability may arise with particular medium properties, computer architectures, or software implementations. Having analyzed wavefield modeling performance in detail, we then quantified the realistic costs associated with the imaging condition in RTM, especially extended imaging conditions. For large extensions of the imaging condition, the associated cost dominates the total execution time and adds very significantly to the total cost of the migration. Our implementation targets both shared and distributed memory parallelism, making it suitable for general CPU clusters, nonuniform memory access architectures, and Intel Xeon-Phi. We have also discussed other aspects of our implementation in detail. In particular, we have explored an alternative method to achieve concurrent communication and computation in RTM.