I have checked FreeBMD (
http://www.freebmd.org.uk/cgi/search.pl) and I believe this many be your man:
Hillman Reginald Sydney Christchurch 2b 684
His name: Reginald Sydney, his birth was registered in the June quarter for the year 1908. It was registered at Christchurch and is in volume 2b on page 684. You can order his birth registration from the record office. To do that you can look here:
http://www.freebmd.org.uk/Certificates.htmlI then checked for a marriage of a male HILLMAN and a female PLUMB. I found this: Marriages Dec 1901
Hillman William Sydney Christchurch 2b 1545
Plumb Alice Christchurch 2b 1545
Note the second name Sydney for William.
This couple had their marriage registered in the December quarter of 1901. Unfortunately they won't be together in then 1901 census, but you might be able to see them with their families. Checking for other HILLMAN births between the December quarter 1901 (possibly even before) and the quarter for Reginald's birth might give you the names of other children born to the couple. Registrations were registered for three month time periods, so the first quarter would be registered January to March. This isn't necessarily the time period the event happened, but it is usually close. If you order the certificates I believe they are approximately 10 pounds each. You CAN specify that you only want them if the mother's maiden name is PLUMB. I am not sure exactly how that works, but the page I linked my tell you more.
I believe William may be the William S HILLMAN living at #2 Dorset Place in Bournemouth in 1901. This William is a cabinet maker aged 27 (and born Cornwall). He is a boarder in #383 of the schedule. West Cliff, Bournemouth, (Christchurch)District 2, in Hampshire page 51 (or 54 - both numbers are on the top right corner). I don't know that they married early enough for any children to be eligible to sign up for the war, but you can try. I have to go as I'm supposed to be packing to leave, but if you send me an email at genesaplenty at gmail dot com I will try to find something else for you and give you more ideas on where to look. I believe I have found Alice in Bournemouth as well. She is with her family, which is helpful for later when you want to follow her line.
Maer