... in the correct spot, but when you create a blueprint of a single accumulator it doesn't place ... the boiler) only exibit the behavior when you tile from that direction.

Expected behavior: when ... odd tilings just work the moment the render shifts to a valid position.

See video "Screen ...

For some reason selecting new blueprint contents for a blueprint that has an absolute grid will destroy your offsets. Especially when rails are involved ... blueprint (the red flag) being in a different place. By my eye, off by 1 tile south and 1 tile west.

I have the following vanilla mods enabled:
Base ...

... coords must be odd, and the horizontal distance from the leftmost tile/entity to the leftmost rail entity must be odd. Similarly for topmost.

So in your posted blueprint, I think it's the topmost signal that's causing the problem.

Examples of problem blueprints (all with odd grid position ...

Description:
When rotating a blueprint that has an odd size (for example 1x1 or 3x3) the blueprint is shifted by 1 or 2 tiles.

Reproduction scenario:
Have a burner-inserter and a blueprint in your inventory (for example ... not centred under your cursor and shifts 1 or 2 tiles).
Expected result ...