A transfer from a checking or current account to a savings account is not in the budget

Transfers go between two accounts. When both of them are 'budget' accounts - ie, marked so in their account details, then transfers between them do not appear in the budget. This is because the budget is really one big pot of money and what you're doing is the equivalent of taking it out of a pocket and putting it another. This implies moving money within the budget makes no difference to the value that you have available to you.

When you remove one of the accounts (use the account details to uncheck the option to mark the account as a budget account), then the money is being removed (or added, depending on the account removed) from the budget and an entry will be shown in the budget to mark this as the equivalent of taking the cash out of your pocket and putting it somewhere you can't get at it immediately.

So, in this case BOTH accounts are in the budget. If you need to see the money coming out of your budget, then your savings account is probably better off moved out of the budget. You'd then see a 'transfer out of budget' line in the budget properly reflecting this.

See also Article 133.