With your seat higher, your centre of gravity has got higher, and there's now more load on your handlebars (assuming you are bearing more of your weight on your arms now that your handlebars are lower). This means you're also putting more weight above your centre of gravity, rather than most of the force going down the saddlepost.
I'll stop there... the only other thing I know about down forces involves flying buttresses and gargoyles.
I'm sure there will be others along in a while to offer a more technical explanation.
On the whole, I wouldn't call that a good thing, no.
It sounds like your pedalling action lacks the smooth precision of a well oiled machine.
When I was new to cycling my legs lacked the suppleness needed for a good rate of rpm and I used to bounce around somewhat in the saddle. This amused my fellow cyclists who were more proficient and although older, more supple.
Take my advice...visit www.bikefitting.com, find your nearest participating bike shop, get along and get yourself properly measured for bike set up, it'll be the best £35 you ever spend on your bike.
I found out I was on a bike that was too small for me, some adjustments were made, new stem, higher seat post, which made a lot of difference, ultimately I went out and purchased the carbon dream machine I had always lusted after.
The dealer AW Cycles refunded the cost of the fitting against the cost of the new bike, so the fitting was free, result I now have a gorgeous Wilier Mortirolo carbon framed bike, with a sexy Campag Centaur groupset, that fits like a glove (well bike actually!)
Set to my style of riding sport/fitness, which means I can ride the bike efficiently and in comfort.