The new service started a month ago so I doubt if you will find a forum member who has used it yet. I did the journey in November. The best bit of advice I can give you is avoid the train across the causeway unless you specifically want to use it. Woodlands metro station is a mile or so away from Woodlands railway station (next to the checkpoint). Its easier just to get the bus from Woodlands Metro, go through the checkpoint and get back on the bus which takes you to the Malaysian checkpoint. JB Sentral is within the same building, once you have passed through Malaysian border control there are clear directions to it.
Coming FROM KUL I assume its now elektrik ''steamcar'' (thats literally the Malay word for train=kereta api) until Gemas and change to what I assume are the remains of the old through trains onward. As explained: in JB the stesyen is In the giant new border check-post (stock up if any food is needed, its much cheaper as in SIN), pass thru Malay emigr, then find the busstops-there are 4: SJE Ekspres IN SIN proper, ditto from SBS, and both SBS and what used to be Causeway (may have changed) to the nearestby Metro station in SIN-SIn Immi is at their side of the causeway-if you like you can also walk over it, but it wont save on busfares (as in MY you can pay-cash only, farebox, with MYR). There may be giant jams on that causeway later in the day-do allow for plenty of time if you intend to fly out of SIN straight-away.