Recently, I have found some literature which does help to answer my question.
On p. 339, Clayden, Greeves, & Warren (2012) did mention that in general, $\alpha$- nitrogen, as well as sulfur, substituents can effectively provide resonance stabilisation to the carbocation, facilitating the $\ce {S_N1}$ process.

Similarly, on p. 433, Carey & Sundberg (2007) mentioned :
Adjacent atoms with one or more unshared pairs of electrons strongly stabilize
a carbocation. Table 3.11 (p. 304) indicates the stabilization of the methyl cation by such substituents. Alkoxy and dialkylamino groups are important examples of this effect.

More interesting information
When we see such circumstances of resonance stabilisation, I believe many of us may question to what extent is this effect at play because this seemingly goes against conventional understanding as more electronegative atoms are bearing the positive charge. To this, Carey & Sundberg (2007) went on to say:
Although these structures have a positive charge on a more electronegative atom, they benefit from an additional bond that satisfies the octet requirement of the tricoordinate carbon. These “carbocations” are best represented by the doubly bonded resonance structures. One indication of the strong participation of adjacent oxygen substituents is the existence of a barrier to rotation about the C−O bonds in this type of carbocation.
If you think about it, it does make perfect sense since you are making an extra bond through this resonance effect. The exothermicity of bond formation more than compensates for the placement of the positive charge on the electronegative atom.
References
Carey, F. A., & Sundberg, R. J. (2007). Advanced Organic Chemistry Part A. Structure and Mechanisms (5th ed.). Springer.
Clayden, J., Greeves, N., & Warren, S. (2012). Organic Chemistry (2nd ed.). New York : Oxford University Press Inc.