Yes, WatchLOI's payment processing system is extremely safe and secure. Payments are processed by Stripe, which has been audited by a PCI-certified author and is certified to a PCI Level 1 Service Provider. This is the most stringent level of certification available in the payments industry. To accomplish this, they make use of best-in-class security tools and practices to maintain a high level of security.
For more see Stripe's security information.