Deleting an app does not cancel the subscription if it has one. You must cancel the subscription:
View, change, or cancel your subscriptions - https://support.apple.com/HT202039 - "Your membership or subscription might renew if you don't cancel your membership or subscription more than 24 hours before your renewal date." At this stage the renewal is considered a purchase. For a new subscription the sale is probably effective from when you first agree to subscribe.
Apple's terms of purchase in the USA are, "All Transactions are final" (https://www.apple.com/legal/internet-services/itunes/us/terms.html), but some countries have different laws so check terms for your country at: http://www.apple.com/legal/internet-services/itunes/. If sales are final then it is Apple's decision if they want to grant a refund. You can always ask, and people do get refunds on a case by case basis, but Apple can also say no. To request a refund:
Get help with an item purchased from the iTunes Store, App Store, Mac App Store, or iBooks Store - https://support.apple.com/HT204084
Report a Problem - http://reportaproblem.apple.com - "Sign In for help with iTunes purchases made in the last 90 days"
Other ways to contact iTunes Store Support: