Ceiling Light Wiring Confusion
Your description is somewhat vague but I'll give it a try.

You say there are four wires from the house. I'm going to assume that these were connected together in pairs. In turn, each pair was connected to wires going to the old lights.

If the above is not correct, STOP READING! You need to clarify the wiring to us. A photo or drawing may help.

One of the pairs of wires is HOT and the other is NEUTRAL. Unfortunately, due to the lack of coloring, it may be difficult to tell which is which. Do you know that one of the pairs was connected to the outer ring of each socket? If yes, that pair should be NEUTRAL. If no, do you know which pair was connected to the old pull switch? If yes, that should be HOT.

If neither of the above can be determined, I strongly recommend you call an electrician to sort it out to avoid setting up a hazardous situation.

Assuming that has been sorted out, the wiring should be as follows:

HOT to one black wire of the switch. The other switch black connects to both blacks on the sockets. The white wires on both sockets connect to NEUTRAL.

I'd also recommend getting a roll each of black and white electrical tape. Wrap a strip of black tape on both HOT wires coming from the house. Wrap a strip of white tape on both NEUTRAL wires coming from the house. this will correctly identify the wiring for the future.

Again, if anything I've written does not match what you know of the wiring or if anything is not clear, STOP and call an electrician. If you connect things incorrectly, you could be setting up a very hazardous situation where someone could be electrocuted or your house could catch on fire.