How to choose an interpolation method for seismic ground motion signals
If there are differences then some likely sources might be  that the window on the Sinc wasn't wide enough, that the data wasn't really sufficiently bandlimited, or too much quantization noise in the samples.

The double integration of anything with system offsets or quantization noise is unlikely to be zero. (See random walk) One solution would be to compute the double integral of the first pass interpolated result and then bias the interpolator (noise filtered if needed) until the resulting double integral goes to zero.