I don't know about other energy suppliers but with eon-next there should be a warning that if you change your tariff your IHD will not be updated unless you pester Customer Services.
11 days after my tariff changed my IHD was still using the old rates, I contacted Customer Services yesterday and my Electricity has updated, but not Gas. I'll give it another 24 hours for the Gas to update but my expectations aren't exactly high.
Now here's a thought, imagine gas and electricity prices dropped dramatically rather than them having gone rocketing upwards, I wouldn't mind betting that IHDs would be updated immediately without problems, because if it's cheaper you want customers to use more. The longer it takes the customer to see a higher cost of watching TV for example then the longer it takes before they start start cutting back.
As I said, it's just a thought. When businesses struggle to do the simple things then I get a bit cynical, and mischievous!