This connection is not acceptable without a steel connector. It’s not complete, but I don’t know how it could be finished properly.
I hate this kind of construction, because it relies on the installers craftsmanship.
Those “notches” are from the carpenter “dapping” the main support beams (double P.T. joists) into the column. Dapping is fine if 1) it’s done properly, 2) if the remaining wood portion is acceptable, and 3) there’s a proper connection.
1) Dapping into the column is critical because if ANY of the horizontal cuts extend too far into the column, it reduces the “effective” size of the remaining column. That is to say, if any cut is too deep, it ruins the column. If the column is a 6x6 and the horizontal beam is dapped 2 1/2” into the column leaving 3” in each direction, then there is something smaller than a 4x4 remaining.
So, if a horizontal cut is 1/4” too deep, you have a column that cannot support that kind of load without a steel connector.
2) Wood columns have imperfections. If a knot hole occurs in the remaining portion, it cannot support the load and is not acceptable for securing the beam to post. (It’s difficult to see in the picture, but there appears to be a large knothole at that location.)
3) The reason steel connectors are used is because they transfer the load properly. The 3 nails showing in the first picture is not acceptable. (Ask your builder if there’s a steel connector planned for the connection.)
In addition to the “notch” issue, the beam consists of two P.T. Joists sandwiched together, but they are not nailed together properly. I know it’s under construction so it’s not finished, but I’d want to know how if they are going to be nailed together. (There are only 3 nails about 6’ from the corner. This is not acceptable. I’d ask if the deck beams are to sit on top of these double P.T. joists or framed into the side of it. I suspect they’ll be framed into the side of it and therefore only one of these joists will carry the deck. This is not acceptable because the vertical posts are too far apart to support the load with just one of the double joists.)
Structural design is not just holding things up, but also holding things laterally. No nailing or bolting pattern into the remaining 3x3 is acceptable for this (especially for two directions.) A steel post connector is required.