Kirknewton LC is of the MCB-OD type, as is Kingsknowe, which is of a very similar design a few miles towards Edinburgh. The only difference being the Limit of Shunt (at Kingsknowe) and differing treadle type/layout. Both have junctions just ahead, are at stations, and have a mix of traffic. They were both upgraded from AHB nearly 10 years ago due to the horrendous amounts of misuse they experienced.
If the signaller at Workstation 4 sets a route up to the signal protecting the crossing, then the train will be brought to a stand and the driver will have to use the plunger to activate the crossing (unless the signaller intervenes, which they may do if there is a problem). If the signaller sets a route through the crossing and also indicates that the train is not stopping, then the barriers will be lowered in the normal sequence. *Note, that for the signaller, you can also read ARS (Automatic Route Setting). The system will then (either by plunger or signaller) activate the sequence, including the use of Obstacle Detection to prove the absence of any obstruction on the railway. It is very sensitive, and will detect anything from a blowing plastic bag to a vehicle, to a very slight deflection of the booms (usually because a vehicle has clipped them).
A train approaching either is brought to a stand through the normal sequence of approach, including the use of Overspeed sensors for the TPWS. Overrun treadles will place the barriers into failed mode and immediately illuminate the flashing red lights (which as all motorists know means "DO NOT PASS" under any circumstances). If a train does overrun the signal, it will be at relatively low speed because it will either be having had a full emergency brake application from linespeed at the overspeed sensor, or has somehow slipped past the trainstop sensor, at which point it will have been doing a lower speed anyway.
In my 17 years signal engineering experience, Kirknewton and Kingsknowe have the best Hi-Def, night vision equipped, CCTV systems I've ever encountered, and have led to many prosecutions and the ability to disprove allegations against our equipment, which is always the first line of defence following any visit from the BTP. The combination of that, with our data recorders, ScotRails station and on-board CCTV, makes me wonder why anyone would risk it.
But to answer the OP, its a very normal sequence of operation and while less common now, LX at stations used to be a very regular feature of our network. But I guess it could be jarring if you weren't expecting it. Wait until you experience trains occupying both platforms as you drive over.