To determine if the hotfixes have been applied correctly -

For 3878 - the java hotfix:
Ensure the following folder is in place:
\ECC\tools\JRE\Nt\1.4.2.3878
Also, once you've applied the hotfix correctly - when you navigate to the installation page (eccserver:30000) you will see the hotfix for DST ready to be applied to the console.

For 3862 - the oracle patch:
I rebooted the server for my test.

Once we've adjusted to DST - I suppose that will be the final test ...

Regards,
jq