When creating a problem (graphically), it is impossible to make the new problem _not_ appear on the main site: there is no "problem is active" checkbox on the "Add Problem" page.
Suggestion: if the problem is added to the sandbox
("Select to make part of your sandbox play area" is selected on the Add Problem), then:
1. automatically mark the problem "not active",
2. make the word "problem" in "Problem added to sandbox" a link to the problem (&undead=1)
3. make the word "sandbox" in the same sentence a link to that user's sandbox.
{Posted by bass}