So how did the police know he had just purchased firearms and what kind?
In Oregon FFL's have to report all firearm sales to their local and state PD.
http://www.nraila.org/statelawpdfs/ORSL.pdf
All dealers, pawnbrokers or otherwise must keep a record of
every handgun sold. This record shall contain the time, date and place
of the sale or trade, the name of the salesperson making the sale or
trade, the make, model and manufacturer's number on the handgun.
The purchaser must sign his name and affix his address to the register.
Thumbprints are taken. The purchaser must present clear evidence of
his identity.
A copy of the record must be mailed to the local police and state
police on the day of the sale for a record check.
A gun dealer shall request by telephone that the Dept. of State
Police conduct a criminal history record check on the purchaser. The
Dept. of State Police shall immediately or by return call determine
whether the purchaser is qualified to complete the purchase. The
fee for the criminal history record check may not exceed $10. The
handgun must be unloaded when delivered.