Yes, a user can upgrade their subscription from their dashboard. The charges will be based on pro-rata basis of their current plan in this case.
For example, if you upgrade from the Starter plan to the Standard plan after 7 days, then a user will be charged the $(79*7/30) = $18.43 for this subscription. The remaining amount i.e. $60.57 will be adjusted against their new plan. So they will be charged $199-$60.57 = $138.43 on the date of account upgradation. This amount will be deducted from their credit card.
Please note that this will change the billing date.