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Tag group rates are targets, not exact, and do not have precise start times. They run at the best effort pace of their contents. You cannot control the "offset". Look at individual device status pages to see how closely the device is achieving the paces requested.
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Tags pointing at the same processor and same top-level tag will be optimized to be read together only if using the same pace. This is how you minimize network (and PLC) load. It doesn't matter if there are many tag groups--it matters if the pace differs.
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Optimization is brand- and driver-specific. For modern Allen-Bradley, this discussion (and the links within) may be helpful: