To build the primary I took a piece of 20cm wire, then bent it at the middle (10cm) and fold it back so I can have a bifilar wire. Then I wound this bifilar winding on the primary. So the winding starts from the start of one of the wire ends, and then ends to the folded point, then continues backwards into the other wire end. The two wire ends are the connection points of the primary. The folded point is left unconnected.
If I understand right, you are trying to build a saturable reactor. The type shown in the first link can't be build on a single core. Sending current back forth through the bifilar winding has just just zero effect.
The diagram is a saturable reactor (as described in the linked article). (AKA magnetic amplifier.) The dots indicate orientation of the windings. The DC side (control side) has its windings oriented so as to suppress AC induced in them from the AC side (power side).
Seems as though you wound the DC turns correctly. The article states you can have a single core despite the diagram showing two separate cores.
This phasing of control windings can be accomplished with two separate reactors as shown, or in a single reactor design with intelligent layout of the windings and core.
If I understand right, you are trying to build a saturable reactor. The type shown in the first link can't be build on a single core. Sending current back forth through the bifilar winding has just just zero effect.