Ord made the first survey and laid out the first grid in 1849. The Spanish did no survey and did not lay out any grid.
The change in angle is because of the edge of the Spanish one-league square land grant. However, there is no Spanish grid. All grids were laid out by American surveyors according to American rules.
The reason the angle changes at the edge of the land-grant is because that was the city limits when they surveyed the city. When more land was annexed, it was surveyed, too, and the expansion was laid out to true north.
The reason for the odd angle inside the old city limits is because Ord aligned Main Street to the edge of the bluff up from the river, to keep the city above flooding. Then, he aligned the grid to Main Street.