Irrigation is a key factor for different physiological aspects of fruit trees. Therefore, such irrigation protocols that can save water consumption during irrigation and maintain fruit trees productivity are an essential goal especially under semiarid climate conditions. The aim of this 3-year apricot study was to investigate the effect of four deficit irrigation (DI) treatments (control, moderate regulated deficit irrigation: RDIm, severe RDI: RDIs and continuous DI: CDI) on 15 tree physiological properties (chilling requirement—CR, heat requirement—HR, days from end—dormancy until fruit harvest—DEDFH, sum of growing degree days—sGDD, total number of buds—TNB, number of flower buds—NFB, number of vegetative buds—NVB, starting date of flowering—SDF, number of opened flower buds—NOFB, flower bud abscission—FBA, fruit set—FS, seasonal vegetative growth—SVG, fruit number per tree—FNT, fruit weight—FW, fruit yield—FY), and on two tree chemical properties (total soluble carbohydrates—TSC and total proline content—TPC) on apricot cultivars ‘Ninfa’ and ‘Canino’ in Egypt. Results showed that both DI treatments and cultivars significantly influenced the values of CR, HR, TNB, SDF, NOFB, FS, SVG, FNT, FY, TSC, and TPC. Values of FBA were significantly affected by years and DI treatments, while sGDD by years and cultivars. Values of DEDFH, NFB, and FW were significantly influenced only by cultivars, while NVB only by DI treatments. The RDIm treatment gave the most acceptable values for most measured properties compared to the fully irrigated control treatment. Prediction based model analysis demonstrated that generalized linear models (GLMs) can be predictors for the measured tree properties in the DI treatments. The best goodness-of-fit of the predicted GLMs was reached for HR, NOFB, FS, SVG, FNT, TSC, and TPC. In all the four DI treatments, 22 pair-variables (TNB versus (vs.) NFB, TNB vs. NOFB, TNB vs. NOFB, NFB vs. NOFB, NFB vs. FNT, NFB vs. FY, NFB vs. FW, NOFB vs. SVG, NOFB vs. FNT, NOFB vs. FY, FS vs. FNT, FS vs. FY, SVG vs. FNT, SVG vs. FY, SVG vs. TSC, FNT vs. FY, FY vs. FW, CR vs. TSC, HR vs. TNB, HR vs. NFB, HR vs. FNT, HR vs. FY, and NOFB vs. FBA) correlated significantly in Pearson correlation and regression analyses. Principal component analyses explained 82% of the total variance and PC1, PC2, and PC3 explained 23, 21, and 15% of the total variance and correlated with the HR, TNB, FS, FNT and FY; FBA, SVG, TSC, and TPC; and NFB, NVB and NOFB, respectively, indicating strong connections among tree physiological and chemical properties. In conclusion, DI techniques using moderate water deficits can be managed successfully in apricot production under semiarid Mediterranean climate conditions such as the one in Egypt.