By coincidence, I ran into your previous posting of this question just last night (for future reference, if you want to make sure I see a question make sure it has 'Taiping', 'Qing' or 'China' in it), and that led me to have a think about it, so now I've had a trawl through the sources.

So, what are those sources? As for primary sources on Hong Xiuquan's interactions with Issachar Roberts, there are at least five:

1. A letter from Issachar Roberts to William Buck, dated 27 March 1847 and published in a Baptist periodical on 29 July;
2. A piece by Roberts published in the Chinese and General Missionary Gleaner, dated 6 October 1852 and published in February 1853;
3. Theodore Hamberg's The Visions of Hung Siu-Tshuen, published in 1854 based on testimonies of Hong Xiuquan's cousin Rengan in 1852;
4. An account of Hong Xiuquan's life and character titled 'Tae Ping Wang', written by Roberts and published in Volume VIII of the American periodical Putnam's Magazine in October 1856; and
5. The Taiping Heavenly Chronicle, commonly attributed to Hong Rengan and published in 1852.

Accessing these would not necessarily be easy, but is possible. I'll be reproducing all the relevant sections from them anyway, but just for those interested in digging deeper:

1. This I have not been able to find in digitised or published form. There are quotations and excerpts in the Coughlin and Pruden dissertations, cited below.
2. This is reprinted in Clarke and Gregory's Western Reports on the Taiping, where it is document 11, starting p. 19.
3. This can be found scanned via HathiTrust.
4. This can be found scanned via HathiTrust.
5. This can be found in translation in Michael and Chang's The Taiping Rebellion, where it is document 17, starting p. 51. There are scans of the original Chinese text in the University of Cambridge Digital Library and on the Chinese Text Project.

As for secondary sources, the account in Spence's book mainly draws on a 1972 PhD dissertation by Margaret M. Coughlin titled 'Strangers in the House'; I was also able to find another dissertation by George Blackburn Pruden from 1977 titled 'Issachar Jacox Roberts and American Diplomacy in China during the Taiping Rebellion' that also covers those events, drawing on Coughlin. Coughlin cites an earlier article, 'Issachar Jacox Roberts and the Taiping Rebellion' by Yuan Chung Teng in The Journal of Asian Studies, Nov., 1963, Vol. 23, No. 1. Incidentally, this in turn cites an account cited in a secondary piece that was in turn reproduced in a book by Jen Yu-Wen that I don't have on me, so there is presumably a sixth primary account somewhere that I can only refer to rather than quote outright.

For our purposes, it is primary sources 2-5 that are of interest (the letter to Buck being written before Hong left). Seeing as the discussion of Hong's time with Roberts in them is generally quite short, it seems prudent to reproduce the relevant sections, and then work through their implications.

Roberts' piece in the Chinese and General Missionary Gleaner says the following (note: Roberts here refers to a 'narrator' and 'narrative', these are Hong Rengan and the piece by Theodore Hamberg, respectively, which Roberts had seen the manuscript of):

...Some time in 1846, or the year following, two Chinese gentlemen came to my house in Canton professing a desire to be taught the Christian religion. One of them soon returned home, but the other continued with us two months or more, during which time he studied the scriptures and received instruction, and maintained a blameless deportment. That one seems to be this HUNG SAWCHUEN [derived from the Cantonese pronunciation] the chief; and the narrator was perhaps the gentleman who came with him, but soon returned home. When the chief first came to us he presented a paper written by himself, giving a minute account of having received the book of which his friend speaks in his narrative; of his being sick, during which he professed to see a vision, and gave the details of what he saw, which he said confirmed him in the belief of what he read in the book. And he told me some things in the account of his vision which I confess I was then at a loss, and still am, to know whence he got them without a more extensive knowledge of the scriptures. He requested to be baptized, but left for Kwangsi [Guangxi] before we were fully satisfied of his fitness; but what had come of him I knew not until now.

Hamberg's pamphlet says this:

[An associate of Roberts sent a letter to Hong Xiuquan in late 1846 inviting them to meet Roberts, but they were still employed as schoolteachers and would not be able to make time until early the next year.]… Siu-tshuen and Hung-Jin went to Canton, to study the doctrine with Mr Roberts. They were received in a friendly manner, and soon after met with other Missionaries, who also were glad to see them. Having continued their studies about a month, Mr Roberts sent two of his Chinese assistants, Choo and Tsen, with the Hungs to their native place. Here they preached a few days and then returned to Canton, but Hung-Jin, who was well aware that two other assistants of the name Wang, also engaged by Mr Roberts, were making intrigues to prevent new brethren from being employed, for fear of losing their own situations, did not again go to Canton, but remained at home and studied medicine. Siu-tshuen again went to Canton in the company of the two assistants of the Foreign Missionary and continued his studies for some time. The two assistants, Wang-ai and Wang-khien, probably fearing that Siu-tshuen, with his superior talent, would also after his baptism be employed by Mr Roberts, and they themselves lose their position, now planned an intrigue to get rid of him, and prevent his being baptized, in which they succeeded. Pretending to be interested in his welfare, they advised him to speak to Mr Roberts before his baptism, and get the promise from him of a certain sum of money per month for his support, whereby he would be enabled to continue his studies, and remain in Canton, after he had received baptism. Siu-tshuen being very poor, considered their advice reasonable, and acted thereupon. Upon his arrival at Canton, he had frankly and openly presented to Mr Roberts an account of his former life, his visions, his sickness, his preaching, and religious compositions; he now in the same open manner asked Mr Roberts to support him after his baptism in order to enable him to continue his studies with the other assistants. We are not aware that Mr Roberts at that time paid much attention to the written account or papers presented to him by Hung, nor does it seem that he placed any confidence in his statements, or understood his real character; but hearing him, like so many other Chinese candidates for baptism, enter upon the subject of future support, Mr Roberts was displeased, and postponed his baptism until some future uncertain period.

Siu-tshuen felt rather disappointed at this result of his request, and discovered, too late, that he had fallen into the snare laid for him by the two Wang. Being unable to support himself in Canton, and not knowing when he might be admitted to baptism, he resolved to leave and go to Kwang-si without waiting for baptism from the hands of the foreign Missionary. Choo-thau-hing advised him to return home if he would not remain in Canton, but finding him decided in his mind, he gave him a hundred cash, and sent a letter to Hung- Jin in Hwa-hien, informing him and other relatives of Hung-Siu-tshuen, that the latter had left Canton and gone to Kwang-si in search of his friend Fung-Yun-san [Feng Yunshan].

In the sixth month of 1847, Siu-tshuen started upon his second tour to Kwang-si.