The present study develops and optimizes a jet-cutting encapsulation method using a laboratory-scale encapsulator to incorporate herbal dietary supplements into fermented milk products. Sodium alginate and pullulan were selected as core and coating polymers, respectively, after rheological screening demonstrated that 1% alginate (η ≈ 350–450 Pa·s at 22–25 °C) and 2% pullulan (η ≈ 400 Pa·s at 25–30 °C) provide a balance between atomization, shell integrity, and fluidity. Under optimized conditions, capsules of 1.00 ± 0.05 mm diameter and high sphericity (aspect ratio 1.08 ± 0.03) were produced. In vitro gastrointestinal simulation confirmed capsule stability in simulated gastric fluid (pH 2.0) and complete disintegration within 120 min in simulated intestinal fluid (pH 7.2). Inclusion of 8% (w/w) capsules in a fermented milk beverage preserved appearance, texture, flavor, and color while increasing viscosity from 2.0 to 4.0 Pa·s. Titratable acidity rose from 87 °T at 24 h to 119 °T at 120 h, with sensory quality remaining acceptable; substantial gas formation and excessive sourness occurred only after 168 h, defining a 5-day refrigerated shelf life. These findings demonstrate that the 1% alginate–pullulan capsule system successfully protects plant extracts during gastric transit and enables targeted intestinal release, while maintaining the sensory and rheological properties of the fortified fermented milk product.