A question about direction of x-axis in backbone frame construction

Hi! I have a question about the construction process of the backbone frame.

In the section 1.8.1 of the supplementary of the AlphaFold2 paper, it says that you use N as x1, Cα as x2 and C as x3 and the frame has Cα at the centre. According to the Algorithm 21, the direction of the x-axis will be from Cα to C.

However, in the implementation, the coordinates of C atom are passed as the negative x-axis. So it seems that in practice, the x-axis will be from C to Cα.
https://github.com/deepmind/alphafold/blob/918434f597c0f8a7bd999f878de474aeb0a0b4ae/alphafold/model/all_atom.py#L202-L206
https://github.com/deepmind/alphafold/blob/918434f597c0f8a7bd999f878de474aeb0a0b4ae/alphafold/model/r3.py#L73-L96

What makes me confused is that in the constant array `rigid_group_atom_positions`, the x-coordinate of C relative to the backbone frame is positive, which implies that the x-axis should be from Cα to C.
https://github.com/deepmind/alphafold/blob/918434f597c0f8a7bd999f878de474aeb0a0b4ae/alphafold/common/residue_constants.py#L126-L133

I'm not sure where I have made a mistake. Could someone help point it out?